#### Chen

Ok, I'm currently reading a book about VSL and it mentions relativity at the beginning, and while reading I couldn't help but wonder something... in a nutshell it says that since light has a finite speed (and not infinite), time must be relative. It gives the example of how when cows who stand by an electric fence jump back from it as soon as it was activated, it looks different from different perspectives, i.e the person who stands on one end of the fence will see all cows jump "at the same time" while another person on the other end of the fence will see them jump "one at a time". (Obviously this is exaggerating, and assumes that electricity propagates as fast as light travels, but you get the picture.)

My question is this... sure this means that things don't seem to happen at the same time, but that's only because we are using our sight to determine what happens when. But in reality everything still happens at the same time... or not?

(I'm aware that this is probably a stupid question that I only have because I've not studied relativity as a physicist but just read about its key ideas from a book, but still an answer would be nice. :) And I also hope I posted this in the right forum...)

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#### Hurkyl

Staff Emeritus
Gold Member
One of the key differences between special relativity and nonrelativistic mechanics is that "at the same time" is observer-dependant. It only makes sense to say "In this particular reference frame, the events were simultaneous", it does not make sense to say "the events were simultaneous".

Hurkyl

#### Chen

Yes, that much I already understood. :) But here's what baffles me... every particle can be described as a point in space-time, right? But if the same thing happens not at the same time, doesn't it mean that the same particle must exist in two different points in the space-time dimensions?

(Also there was a typo in my original post; it said 'time has a finite speed' which is obviously wrong.

#### LURCH

Not a dumb question at all!

You see, time is nothing but the movement of things. As you have already learned, the movement of things may appear different from different perspectives. I think the peace of the puzzle you're missing is the fact that the "appearence" of an event is another way of saying, "the arrival of light (and all information that travells at lightspeed) from the event". Now information cannot (as far as we know) travell faster than light, so an event can have no effect prior to its "appearence". So the event cannot in any meaningfull way be said to exist prior to its appearence. So to say that the event had not yet occured "form a certain point of view", is just as valid as to say it has occured from some other point of view. If all points of view are equally valid, we cannot say two events were simultanious, but it doesn't look like they are from this perspective.

Now, you might have deduced from all this that your earlier statement about time having a finite speed was not such a big mistake after all. Nor was your use of "speed of light" and "speed of time" interchangably. The speed of light really is, in a quite litteral way, the speed of time!

#### Chen

Ok, I will give my brain a few moments to digest this :), but in the meantime, I do have another question. If I were to travel at space at a speed very close to the speed of light, and had two watches with me - one mechanical and the other digital - what time would they display?

#### Janus

Staff Emeritus
Gold Member
Originally posted by Chen
Ok, I'm currently reading a book about VSL and it mentions relativity at the beginning, and while reading I couldn't help but wonder something... in a nutshell it says that since light has a finite speed (and not infinite), time must be relative. It gives the example of how when cows who stand by an electric fence jump back from it as soon as it was activated, it looks different from different perspectives, i.e the person who stands on one end of the fence will see all cows jump "at the same time" while another person on the other end of the fence will see them jump "one at a time".
There's seems to be a bit of confusion here. If the two observers are just standing at different ends of the fence, they both will see the Cows jump one at a time. It is only when One observer is moving with respect to the other that they will see things differently.

This is due to the fact that light not only has a finite speed, but that speed is the same for all observers.

Let's consider the following example:

You have two observer's, one standing by a railway embankment and one standing on a railway car traveling along the track. Two lightning bolts strike the tracks at equal distances form the embankment observer, timed so that the flash reaches both observers just as two obseservers are lined up with each other. This way, both observers are equal distance from the lightning strikes when they see them and see both strikes at the same time.

From a point just above the embankment observer, things would look like this:

http://home.teleport.com/~parvey/train1.gif [Broken]

Note that the expanding circles of the flash hit both observers at the same time.

Now let's see what happens according to an observer staioned above and moving with the railway car. Again, the lightning flashes must reach both observers at the same time. (this is something that is true for all observers.) But the observer on the train starts closer to one strike than the other and travels while the flashes are traveling. He must also measure the speed of the flashes as constant and equal with respect to himself. Thus for the flashes to reach him at the same time and at the moment his passes the embankment observer, the two strikes cannot occur at the same time. He will see this:

http://home.teleport.com/~parvey/train2.gif [Broken]

Thus for the embankment observer, the strikes occured at the same instant, and for the rail car observer they happened at different times.

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#### Chen

Let me explain the cows example so you can tell me exactly why it's wrong, because it makes sense but I agree that people have to be moving relatively to each other in order to see different things. :)

There is an electric fence in a big field, which is turned off, and there are several cows standing by the fence. Let us assume that electricity in the fence propagates at the speed of light. Person A stans in the right end of the fence, while person B stands at the left end, where the batteries and on/off switch are at. Now person B turns on the fence, and the electricity starts propagating through it at the speed of light, and every time a cow feels it - it jumps (neglecting the response time of the cow).

Now from person A's perspective, since electricity propagates at c, all cows seem to be jumping at the same time - first the first cow jumps in the air, but by the time its image has reached the location of the second cow, it also jumps in the air "at the same time" because the electricity also got to the exact same spot. And so on and so forth until the last cow.

However, for person B the cows all jump one at a time. Assuming the first cow is 1km away from him, and the second cow is 1km away from the first one, then by the time the image of the first cow jumping has reached person B, electricity only got to the location of the second cow, and only after the image of the second cow jumping has traveled 2km will person B see that it has jumped.

Now this makes perfect sense to me...

#### HallsofIvy

Homework Helper
1) electricity does not "propagate at c". An electric current along a wire moves considerably slower than c.

2) If, moving at speed close to c (relative to what?), you are wearing a mechanical watch and an electronic watch they would read the same time because they are moving at the same speed which is the only relevant fact. (I changed "digital" to "electronic" which is what I think you meant. Surely it is obvious that whether the readout is analog or ditital is irrelevant.)

3)
But if the same thing happens not at the same time, doesn't it mean that the same particle must exist in two different points in the space-time dimensions?
Yes, of course. You existed yesterday, you exist today: you exist in two different point in the space-time dimensions. Why in the world would you find that hard to understand?

#### jcsd

Gold Member
Actually Halls of Ivy, it's a long time since I studied this, but IIRC the message velocity in a copper wire is an appreciable fraction of c.

#### Chen

Originally posted by HallsofIvy
1) electricity does not "propagate at c". An electric current along a wire moves considerably slower than c.

2) If, moving at speed close to c (relative to what?), you are wearing a mechanical watch and an electronic watch they would read the same time because they are moving at the same speed which is the only relevant fact. (I changed "digital" to "electronic" which is what I think you meant. Surely it is obvious that whether the readout is analog or ditital is irrelevant.)

3)
Yes, of course. You existed yesterday, you exist today: you exist in two different point in the space-time dimensions. Why in the world would you find that hard to understand?
1) Even so, it's just a theoritcal question. Replace the electric fence with a beam of light that which deters the cows.

2) I guess I don't understand why the watches would show the time in the spaceship and not the time on Earth. How does the fact that they are moving at a great speed change their functioning? Actually, forget about watches. If I were to stand in a space ship that is travelling really-really fast and count "1... 2... 3..." out loud, would 3 seconds pass and why?

3) But me yesterday and me today are not the same thing. I was different yesterday. What I find so hard to understand is how the exact same thing, i.e me today, can exist in two points in time.

#### Janus

Staff Emeritus
Gold Member
Originally posted by Chen
Let me explain the cows example so you can tell me exactly why it's wrong, because it makes sense but I agree that people have to be moving relatively to each other in order to see different things. :)

There is an electric fence in a big field, which is turned off, and there are several cows standing by the fence. Let us assume that electricity in the fence propagates at the speed of light. Person A stans in the right end of the fence, while person B stands at the left end, where the batteries and on/off switch are at. Now person B turns on the fence, and the electricity starts propagating through it at the speed of light, and every time a cow feels it - it jumps (neglecting the response time of the cow).

Now from person A's perspective, since electricity propagates at c, all cows seem to be jumping at the same time - first the first cow jumps in the air, but by the time its image has reached the location of the second cow, it also jumps in the air "at the same time" because the electricity also got to the exact same spot. And so on and so forth until the last cow.

However, for person B the cows all jump one at a time. Assuming the first cow is 1km away from him, and the second cow is 1km away from the first one, then by the time the image of the first cow jumping has reached person B, electricity only got to the location of the second cow, and only after the image of the second cow jumping has traveled 2km will person B see that it has jumped.

Now this makes perfect sense to me...
Okay, In this example it really doesn't matter what each Person "sees happen", but what he determines has happened. In this case, both observers can take what they saw with their eyes, taking into account the propagation delay due to the speed of light, and determine that the cows jumped one at a time and when each Cow jumped. If they were to compare notes later, they would be in perfect agreement as to what happened.

In the train example ( by the way, I fixed the second image link.), Both observers "see" the lightning flashes at the same instant, But one will determine that the actual lightning strikes that caused them occured simultaneously, while the other will determine that they didn't.

Now if they compare notes later, they will disagree as to what "actually" happened.

#### Janus

Staff Emeritus
Gold Member
Originally posted by Chen
1) Even so, it's just a theoritcal question. Replace the electric fence with a beam of light that which deters the cows.
See my response in last post.

2) I guess I don't understand why the watches would show the time in the spaceship and not the time on Earth. How does the fact that they are moving at a great speed change their functioning? Actually, forget about watches. If I were to stand in a space ship that is travelling really-really fast and count "1... 2... 3..." out loud, would 3 seconds pass and why?
For you, three seconds would pass. For someone watching you from the Earth, maybe 3 mins will pass accoring to them. (depending on the speed you are moving wrt Earth.)

Conversely, if you were to watch someone on Earth count out 3 sec, for them it would take 3 sec, but for you it would take 3 min.

Speed does not effect the functioning of the watchs, it effects how the time rate between two relatively moving reference frames appears to each other.

3) But me yesterday and me today are not the same thing. I was different yesterday. What I find so hard to understand is how the exact same thing, i.e me today, can exist in two points in time.
That's because you are still trying to hold on to the idea of time as an universal absolute, rather than a relative measurement.

To you, "you yesterday" occured 24 hrs ago. To someone moving wrt to you, "you yesterday" occured say, 48 hrs ago.

#### Chen

Originally posted by Janus
Conversely, if you were to watch someone on Earth count out 3 sec, for them it would take 3 sec, but for you it would take 3 min.
Unless that is wrong, I just got a whole lot more confused. If someone on Earth counts to 3, 3 seconds would pass for him but for someone traveling very fast it should seem more like 3 miliseconds than 3 minutes? That's what I thought.

#### Janus

Staff Emeritus
Gold Member
Originally posted by Chen
Unless that is wrong, I just got a whole lot more confused. If someone on Earth counts to 3, 3 seconds would pass for him but for someone traveling very fast it should seem more like 3 miliseconds than 3 minutes? That's what I thought.
No, one of the first things to understand about Relativity is that there is no such thing as a "Prefered frame of reference". In other words, you can't say that something is moving very fast without saying what it is moving relative to. And even then, its speed is only ralative to that object.

For example, if you have two objects, A and B and they are moving relative to each other. As far as Object A is concerned, it is object B that is actually moving, But as far object B is concerned, it is A that is actually moving. That is as far as it goes. There is no way to say which of the two is really moving, in fact, the the very question is meaningless.

Thus if the two objects are watching each other's time rates, Since from each's point of view it is the other object that has a high velocity and the other objects time rate that runs more slowly.

This is true for as long as both objects maintain a constant speed with respect to each other.

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